Reconstruction of defects in elastic bodies by combination of genetic algorithm and finite element method

Modeling of the non-destructive testing system of defects in solids is performed. Specifically, the inverse geometric problems of the elasticity theory for a flat rectangular area on reconstructing circular cavities and cracks breaking the body surface are considered. Additional information for solving these problems is a setting of the first four natural resonance frequencies. The inverse problem solution is based on the minimization of the residual functional between the measured input source information and the data calculated during the numerical solution of direct problems with the given parameters of defects. As a tool for solving direct problems, the finite element method implemented in FlexPDE program is used. The functional minimization is carried out by using a genetic algorithm (GA) implemented in the developed GAFEMNDT program. The program algorithm and GA settings used in the numerical experiments are described. The experiments results on determining parameters of defects (coordinates of centre, radius, coordinates of surface cracking and its size) are presented. The results demonstrate adequacy of the additional information to overcome the problem ill-posedness, as well as high efficiency of the proposed algorithm both in accuracy of detecting defects parameters, and in their search speed.